Pathologies of the large- N limit for RPN-1 , CPN-1 , QPN-1 and mixed isovector/isotensor σ -models

Alan D. Sokal, Andrei O. Starinets

    Research output: Contribution to journalArticlepeer-review


    We compute the phase diagram in the N→∞ limit for lattice RPN-1, CPN-1 and QPN-1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.

    Original languageEnglish (US)
    Pages (from-to)425-502
    Number of pages78
    JournalNuclear Physics B
    Issue number3
    StatePublished - May 14 2001


    • Mixed isovector/isotensor model
    • Nematic liquid crystal* N→∞ limit* 1/N expansion
    • Nonlinear σ -model
    • RP model* CP model* QP model* N -vector model

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics


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